Introduction

Mammalian myocardium is a functional syncytium of myocytes coupled by gap-junction (GJ) channels of connexin (Cx) proteins.¹ Experiments with uniform 1- and 2-dimensional cultured strands, as well as computer simulations, show that these channels are important determinants of action potential (AP) propagation,^2,3 concluding that increased GJ electric resistance (R_j) slows AP conduction velocity (CV).

Clinical Perspective on p 1214

The situation in intact myocardium is less clear. One-dimensional cable theory predicts CV to vary inversely with the square root of total tissue axial resistance through the tissue, R_i, corroborated in mammalian ventricle by independent measurement of R_i and CV.⁴ Axial resistance has 2 series components: from the sarcoplasm, R_c, and from GJs, R_j, each significantly contributing to R_i.⁵ Thus, R_j would be expected to be an important and continuous determinant of CV in intact myocardium. At variance with this concept of a continuous relationship between R_j and CV, studies in Cx43-gene knockout mice have shown CV slowing, measured by epicardial optical mapping, only when Cx43 deletion was virtually complete.^6–8 This finding has been widely accepted as a general concept that there is massive redundancy of myocardial GJ coupling. In contrast, there are several reports of significant changes of CV associated with relatively small changes in Cx43 levels in diseased human myocardium and animal models of disease,^9–13 However, the specific relationship between GJ resistance and CV has not been determined systematically, in large part, because the 2 variables have never been directly and independently measured in the same preparations, nor has the contribution from other potential contributory factors that may influence CV. Optical mapping does not allow a quantitative determination of the relationship between CV and R_j, as precise conduction pathways are unclear and R_j cannot be measured. We therefore used techniques to measure directly CV and R_j in a set of complimentary studies to test the hypothesis that in intact myocardium CV is a function of R_j over a continuous range of values commensurate with moderate, naturally occurring ranges of coupling and uncoupling in pathological conditions. We used validated methods,^5,14 to measure R_j and CV and their general relationship in guinea-pig myocardium from different cardiac chambers with and without a GJ blocker, carbenoxolone, and in human ventricular myocardium excised from patients with hypertrophic cardiomyopathy. We also examined the effects of carbenoxolone on local, submillimeter propagation in intact human myocardial propagation as inferred from changes in bipolar electrogram duration during clinical electrophysiology studies to determine how the ex vivo findings are manifest in, and may therefore be inferred from, clinical measurements.

Methods

Preparations: Guinea-Pig Myocardium

Male Dunkin-Hartley guinea pigs (400–600 g) were euthanized and the hearts rapidly excised and immersed in preoxygenated Tyrode solution containing (mmol/L) NaCl 118, KCl 4.0, NaHCO₃ 24, NaH₂PO₄ 0.4, MgCl₂ 1.0, CaCl₂ 1.8, glucose 6.1, Na pyruvate 5.0 (pregassed with 95% O₂/5% CO₂, pH 7.35±0.03); all chemicals were from Sigma, United Kingdom. Left ventricular (LV) trabeculae and atrial pectinate preparations (250–600 µm diameter, 3–5 mm length) were dissected at room temperature. These preparations possess a high degree of cellular alignment^15,16 and are ideal for measurement of CV and resistivity in a single, longitudinal axis.

Human LV Myocardium

Basal LV septum from 6 patients with obstructive hypertrophic cardiomyopathy undergoing surgical myectomy was obtained. Samples were dissected carefully and the section handled by surgical instruments was immediately excised with a sharp blade and discarded. Samples were placed immediately in Ca²⁺-free Tyrode solution at room temperature and preparations dissected in the laboratory within 30 minutes.

A portion of the tissue was also frozen immediately in liquid N₂ and stored at −80°C to measure cell diameter. Guinea pigs were handled in accordance with Guidance on the Operation of the UK Animals Act (1986). Human tissue was used with approval of the local ethics committees and with informed patient consent.

Measurement of Cell Diameter

Frozen, transverse 10-µm sections (cryostat: Thermo Shandon) were mounted on poly-l-lysine–coated glass slides and stained with hematoxylin and eosin. Cell diameters through the nucleus, and the muscle/interstitial cross-sectional area ratio, were measured in ≥10 cells per section, from ≥5 sections per specimen.¹⁷

Measurement of Myocardial Impedance, Calculation of GJ Resistivity, and Estimation of Extracellular Resistance

The method and its validation have been described previously in detail.⁵ Myocardial preparations were placed in a 3-chambered bath; the outer chambers were superfused with Tyrode solution at 37°C, and the muscle in the central chamber was coated with mineral-oil gel. Alternating current (0.02–100 kHz) was passed between platinum (Pt)-black electrodes in the outer chambers; current therefore flowed through the intracellular muscle pathway within the oil-gap, with a fraction through a parallel extracellular shunt. System resistance, r, and capacitance, c, were recorded with a balanced Wien bridge (Wayne-Kerr, United Kingdom). Total preparation impedance, z, was modeled as z=(z_i·r_ec)/(z_i+r_ec), where r_ec is the resistance of the extracellular shunt and z_i is the impedance of the intracellular pathway. r_ec was measured separately by measuring the resistance between 2 Pt-black needle electrodes a known distance apart in the muscle within the oil-gap. Pt-black electrode resistance, r_p, and capacitance, c_p, were measured separately in a large volume of Tyrode solution and subtracted from recorded values of r and c.⁵

Longitudinal impedance, z_i, was analyzed as 2 series components: sarcoplasm resistance, r_c, and GJ impedance, z_j (ie, z_i=z_j+r_c). z_i values were expressed as resistance, r_s, and reactance, −x_s, components (ie, z_i=r_s+jx_s; −j=√−1). Plots of r_s versus −x_s yielded semicircular loci (Figure 1); data were fitted by a circle equation (r_s−a)²+(x_s−b)²=c² (a, b, c constants) to the left-hand locus, using data derived from measurements at 1 to 100 kHz and intercepts with the r_s-axis (abscissa) estimated. This locus derived from the intracellular pathway, whereas the right-hand locus derives from the surface membrane.⁵ The high-frequency (left) intercept is a function of r_c and the right-hand intercept a function of z_i⁵; junction resistance, r_j, was the difference between z_i and r_c.^18,19 Preparation length and radius in the oil-gap were measured. Lower case values of variables (r, x; Ω·cm⁻¹) were converted to specific (R, X; Ω·cm) values by scaling to the proportion of the preparation cross-section area occupied by muscle. The nonmuscle fraction of cross-section area was calculated from the value of r_ec, assuming it was filled with Tyrode solution (49 Ω·cm).⁵ To determine the effects of carbenoxolone, preparations were pretreated for 30 minutes with Tyrode solution + 20 µmol/L carbenoxolone before mounting in the impedance bath, containing Tyrode solution and carbenoxolone solution in the outer chambers.

• Download figure
• Download PowerPoint

Intracellular Electrophysiological Measurements and Measurement of CV

Methods have been described previously in detail¹⁴; preparations were superfused with Tyrode solution (37°C, 4 mL·min⁻¹) in a horizontal trough. Longitudinal CV was measured by stimulating the preparation at 1 end with insulated Ag-AgCl electrodes (10 µs pulses, 1 Hz, 1.5× threshold). APs were recorded at 6 to 10 distances, d, >1 mm from the stimulation site to avoid virtual electrode effects at shorter distances. The slope of the relationship between d and the delay, t, between stimulus artifact and AP upstroke was used to calculate the value of CV; plots were rejected if the r² values were <0.95. At least 2 separate estimates of CV were made in each preparation and were always within 5% of each other. The time constant of the subthreshold AP foot, τ_ap, was calculated from the slope of a semilogarithmic plot of the initial 10 to 12 mV of conducted APs. AP duration was the time from maximum upstroke rate (dV/dt_max) to 50% or 95% repolarization (APD₅₀, APD₉₅) in ventricle and 75% repolarization (APD₇₅) in atrium. dV/dt_max was measured by analogue differentiation of the AP waveform.

After control measurements, continuous intracellular impalements were maintained in Tyrode solution with 20 µmol/L carbenoxolone for ≈30 minutes, or until time of maximal conduction delay and measurements made at regular intervals. A washout of carbenoxolone was commenced after a stable delay had been observed for 5 minutes.

Effects of GJ Uncoupling on Bipolar Electrogram Duration

The influence of GJ uncoupling on local myocardial activation time was determined from the duration of the bipolar electrogram during electrophysiology studies, as a clinically accessible measure of local microscopic CV recorded from electrodes in contact with myocardium. A quadripolar mapping catheter, with 2-mm electrode spacing, created electro-anatomic maps of right atrial and right ventricular activation (Carto, Biosense Webster) during sinus rhythm. Electrogram duration (filtered 30–500 Hz) was measured at >20 sites throughout the atrium and ventricle of each patient before and 1 hour after administration of a single oral carbenoxolone dose (100 mg), which reaches 90% of peak concentration (15 µg·mL⁻¹) within 40 minutes.²⁰ A CARTO mapping system tagged recording sites so that measurements were made at the same locations pre- and postadministration of carbenoxolone. Electrogram duration was measured from the beginning of the first deflection from baseline to return of the last deflection. The study was approved by the local ethics committee.

Statistics

Data are mean±SD. Group comparisons were performed using ANOVA with post hoc analysis using Bonferroni test. The null hypothesis was rejected at P<0.05. Linear and nonlinear curve-fits used a least-squares program (KaleidaGraph, Synergy Software) that with either an in-built subroutine for linear fits (Figure 2) or required the experimenter to add the equation of a circle (above) to estimate parameters from the –X/R plots from impedance data, including initial estimates of the parameters. Pearson correlation coefficients, r², were derived for linear fits and significance was calculated by calculation of t from the relationship: (n=number of data points) and P calculated for n−2 degrees of freedom. Coefficients of variation, c_v, were calculated from sample means, , and SD, s, with correction for small sample numbers: , n=number of samples.

• Download figure
• Download PowerPoint

Results

Guinea-Pig Myocardium: Impedance Values and AP Propagation Velocity

Figure 1 shows a plot of resistance, R_s, versus reactance, −X_s, for a guinea-pig ventricular preparation in the oil-gap chamber. Two dispersions are seen: the partial, low frequency (right-hand) one is attributed to the surface membrane in the 2 outer chambers; the high frequency (left-hand) one to the junction impedance in the intracellular pathway and was analyzed as in Methods.⁵ The intercepts of the high-frequency dispersion on the R_s-axis (R₁ and R₂) correspond to the sarcoplasmic, R_c, and total intracellular R_i, resistivity respectively: the difference between them is a function of gap junctional resistivity, R_j. Table 1 shows control values of R_i, along with its components R_j and R_c. R_i and R_j values were greater in LV compared with left and right atrial myocardium, R_c was similar in samples from all 3 chambers. CV values are shown in Table 2; values were significantly smaller in LV compared with left atrium (LA) or right atrium (RA) preparations. The coefficients of variation, c_v, of the sample data were 3% to 10% for R_i, 2% to 12% for CV, and 6% to 20% for R_j values.

Effects of Carbenoxolone on Intracellular Impedance

Table 1 shows that carbenoxolone increased R_i in all preparations. Examination of the component values of R_i showed that the increase was solely because of an increase of junction resistivity, R_j; sarcoplasmic resistivity, R_c, was not significantly affected. The mean proportional increases of R_j were not significantly different between the 3 preparations (33±5%, 41±4%, and 32±5%; LV, LA, and RA respectively).

Effects of Carbenoxolone on Resting and APs

Table 2 shows that carbenoxolone had no effect on the resting membrane potential, E_m, AP duration or τ_ap. The increase in dV/dt_max with LV and LA preparations (unaffected in RA), and the increase of AP amplitude in LA preparations are consistent with GJ uncoupling causing increased charge accumulation in the cell from which recordings are made, and therefore corroborate this mechanism of action of the carbenoxolone. All significant effects of carbenoxolone were fully reversible after 10 minutes of washout, and there were also no changes on washout to those variables unaffected by carbenoxolone itself. Values of R_i were estimated from 1-dimensional cable theory and were similar to measured values (Table 1).

Quantitative Relationship Between CV and GJ Resistivity

An important objective of this study was to describe the quantitative relationship between junction resistivity, R_j, and AP CV. This addressed the hypothesis that CV is a function of R_j over a range of values that occur under physiological and pathophysiological conditions, and not only when GJ number is almost completely abolished, as is the prevailing interpretation of studies on transgenic mice.

CV also depends on parameters other than R_i: most importantly cell radius, a the initial phase of the AP upstroke (exemplified by the time constant, τ_ap), and a constant specific membrane capacitance, C_m (1 µF·cm⁻²).²¹ Thus, CV values were normalized to allow for influence of a and τ_ap. One-dimensional cable theory defines the relationship between CV and R_i as:

where the constant of proportionality, K, equals a/2C_mτ_ap. Therefore, K/CV² values were plotted as a function of R_i (Figure 2A) using values for R_i, CV and τ_ap from guinea-pig LV, LA, and RA preparations in the absence and presence of carbenoxolone (Tables 1 and 2). Values of myocyte radius, a, were 12.5±0.9 µm (LV); 6.3±0.8 µm (LA), and 6.2±0.9 µm (RA). The linear relationship (r²=0.956; P<0.005) and the intersection near the origin indicate that equation 1 is an excellent description of the relationship between CV and R_i in the absence and presence of carbenoxolone.

Intracellular resistivity, R_i, is further modeled as a linear sum of GJ and cytoplasm resistivities (R_j and R_c). Thus, a plot of K/CV² as function of R_j (Table 1) should also yield a linear plot if R_c is similar in all preparations and in the presence and absence of carbenoxolone (Table 1) with an intercept on the R_j-axis equal to a value of R_c. Figure 2B shows that data were well described by a linear fit (r²=0.946; P<0.005) with data extrapolated to the R_j-axis with a value of 106 Ω·cm. This is similar to the mean of the measured values of R_c shown in Table 1 (125±4 Ω·cm, SEM of 6 mean values, n=6) and further supports this analytic approach to describe the relationship between CV and R_i.

CV is also dependent on the proportion of extracellular space in multicellular preparations.²² Thus, variation between myocardium from different cardiac chambers or in the presence of carbenoxolone may influence the relationship in Figure 2. Histological data showed that the proportion of extracellular space was similar in samples from all 3 chambers (3.3±1.9%, 5.3±1.7%, and 4.7±2.5%: LV, LA, and RA, respectively) and was unaffected by carbenoxolone. Estimation of extracellular space proportion from impedance experiments also showed no variation between chambers (1.7±1.2%, 2.7±1.0%, and 2.4±1.4%: LV, LA, and RA, respectively).

CV and Intracellular Resistivity in Human Myocardium

Having established that the relationship between R_j and CV is similar in both atrial and ventricular guinea-pig myocardium, and with modulation of gap-junctional uncoupling, CV and R_i were measured in human myocardial preparations (Table 3) to determine whether the relationship between CV and R_i is consistent in myocardium from different mammalian species. The human ventricular preparations from patients with hypertrophic cardiomyopathy (Table 3) had higher R_i (P<0.001) and slower CV (P<0.001), longer APD₅₀ and APD₉₅ (P<0.001) and lower dV/dt_max (P<0.05) than guinea-pig ventricular preparations. V_m, AP amplitude and τ_ap, were similar. The single datum point for the K/CV² versus R_i or R_j (Figure 2A and 2B) corresponds well to the guinea-pig data. However, the percentage extracellular space, as obtained from impedance experiments, was 12.6±2.2%, which was larger significantly than guinea-pig data. Thus, the quantitative fit to the data in Figure 2A and 2B was not extended to these data.

Effects of Carbenoxolone on Bipolar Electrogram Duration in the Human Heart

Bipolar electrogram duration in 11 patients undergoing electrophysiology study (Table 4) was significantly longer in the ventricle compared with atrium (48.1±2.5 versus 39.7±4.2 ms). Carbenoxolone significantly prolonged electrogram duration in the right ventricle (53.3±5.3 ms; P<0.01) and in the RA (42.3±4.3 ms; P=0.05), indicating microscopic slowing of CV of an order in the right ventricle (electrogram duration +10.6%) and the RA (+7.0%) similar to the changes in the directly measured CVs in the guinea-pig ventricular and atrial preparations (Table 1). Carbenoxolone had no effect on electrogram amplitude and is consistent with the interpretation that prolongation of the electrogram is because of GJ uncoupling.

Discussion

This study demonstrated a continuous relationship between CV and GJ resistivity, R_j, across different cardiac chambers, in the presence and absence of an uncoupling agent, indicating that R_j is a significant determinant of CV in myocardium. The study design was novel to obtain values for R_j and CV, measured independently in the same preparation. That CV was significantly slowed by moderate increases of R_j indicates there is no threshold of R_j change in influencing CV. This refutes the concept that there is sufficient redundancy of GJ coupling that it takes substantial abolition of GJ coupling to affect CV.

Relationship Between CV and GJ Resistance

Of the factors known to affect conduction, variation of Na⁺ current density was not a significant contributor as there was no association between CV and either dV/dt_max or τ_ap, both influenced by Na⁺ current density.²³ Further, carbenoxolone-induced slowing of conduction produced no significant alterations to AP morphology, other than a small transient increase in left atrial AP amplitude as would be expected with uncoupling. The findings therefore indicate that GJ resistivity, R_j, is the main determinant of CV under the conditions of these experiments. The initial data analysis used 1-dimensional cable theory and 2 factors suggested that this provided a good approximation: (1) the similarity of the estimation of R_c (Figure 2B) and the actual value (Table 1); (2) the concordance between the measured values of R_i (Table 1) and those calculated by cable theory. The latter may be used to calculate R_i from the relation , C_m and τ_m have standard values of 0.9 µF.cm⁻² and 5 kΩ·cm², respectively. This yields mean values of 471, 267, and 203 Ω·cm and may be compared with values of 525, 260, and 220 Ω·cm, respectively, as measured by experiment. Several murine Cx-gene knockout studies showed CV was unaltered by 50% reduction of ventricular Cx43 expression (Cx43^+/− heterozygous mice).^6–8 Only when Cx43 was reduced by ≈90% (Cx43^−/− homozygous mice) was CV slowed by 50%.²⁴ These results contradict both the present investigation and other studies in canine and human myocardium where modest reductions of Cx43 expression resulted in significant conduction slowing.^12,13 Although transgenic studies have provided invaluable insight into myocardial physiology, there remain confounding factors making interpretation of the CV data difficult. These include upregulation of Na⁺ current density²⁵ and a compensatory increase of intercellular coupling via Cx45 channels,²⁶ both of which would attenuate any reduction of CV because of loss of GJs. In the present study, these confounding factors were absent, confirming that R_j is a significant fraction of R_i, especially in ventricular myocardium. It has also been proposed that sarcoplasmic resistivity, R_c, contributes more than R_j to total intracellular resistivity, R_i, so that changes to R_j would have a relatively minor influence on R_i and hence CV.^25,27 However, this study demonstrated that in ventricle R_j is the major contributor to R_i and in atrium contributes equally with R_c. Sarcoplasmic resistivity was constant in different cardiac chambers and in the presence and absence of GJ blockers, and similar to the value measured by independent techniques.²⁸

This lends support to our interpretation that CV is a continuous function of GJ resistivity, R_j, under physiological conditions and in the presence of gap-junctional uncouplers. This study also provides a more detailed explanation of previous investigations, which showed that CV and total intracellular resistivity, R_i, were related over a range of values during conditions such as hypoxia²⁹ and ischemia.³⁰ Further, our results demonstrate that carbenoxolone-induced conduction slowing was because of effects on GJs rather than ion channels, in agreement with previous studies in myocardium.^31,32

The linearity of the function between CV and R_j also shows that 1-dimensional cable theory is adequate on a millimeter scale to evaluate those factors that determine the value of CV in multicellular preparations, where conduction can be confined to 1 dimension.

Comparative In Vivo Measurements With Carbenoxolone

Electrogram duration is a manifestation of local microscopic myocardial conduction.^33,34 We demonstrated carbenoxolone-induced prolongation of the human bipolar electrogram measured from paired electrodes spaced 2 mm apart. The increases in electrogram duration were of a similar order of magnitude to those of conduction delay directly measured in the isolated guinea-pig myocardium. These results indicate that the intact human heart is susceptible to pharmacological uncoupling in a manner similar to isolated preparations. This effect was observed in patients with and without coronary disease in vivo and indicates that the continuous relationship between GJ electric properties and local propagation velocity is independent of a reduced coupling reserve that may exist in disease states.²⁸ These findings accord with studies in mice, in which uncoupling both prolonged the bipolar electrogram and slowed macroscopic ventricular CV.³⁵

Limitations

Although adjacent papillary/pectinate muscles from the same heart were used for the CV and impedance experiments, measurements were not performed on the same actual preparations, and correlations of R_j and CV therefore assume that given their immediate adjacency in the same animal, the 2 preparations have similar electrophysiological properties. Data from 6 hearts (not included) show that CV determination in adjacent ventricular muscles have values within 10%, and from 10 other hearts impedance values were within 5% of each other.

Although cable theory provides a suitable model for conduction in geometrically well-defined tissue, such as papillary and pectinate muscle, it has limitations in modeling conduction in tissues possessing discontinuities such as connective tissue layers that are present in hypertrophic cardiomyopathy myocardium. Therefore, caution must also be applied as proportional extracellular space was greater in these preparations that may confound a direct comparison with the CV versus R_j data from guinea-pig tissue. Although excised normal human myocardium is not easily available, the measurement of electrogram duration in intact, relatively normal human hearts provided strongly supportive evidence of this fundamental relationship.

Conclusions

In intact myocardium there is a continuous relationship between GJ resistivity and CV over a wide range of values such that conduction slowing may occur with modest increases to GJ resistivity. Alterations in cellular coupling of the order that occur naturally can account for variations in electrogram morphology and CV that are of relevance to interpreting clinical measurement and to arrhythmogenic tendency.

Acknowledgments

We would like to acknowledge the ElectroCardioMaths Programme of British Heart Foundation Centre of Research Excellence at Imperial College and the National Institute for Health Research Biomedical Research Centre programme.

Footnotes